Dice Roller

Flat dice and bell curves

The number of dice you roll changes the shape of the outcome fundamentally, and it is the single most important idea in dice-based game design. One die produces a uniform distribution: on a d20, a natural 1 is exactly as likely as a natural 20, and the game feels swingy and dramatic because extremes are common. Roll several dice and add them, and the central limit theorem takes over — the sum bunches around the middle, extremes become rare, and outcomes become predictable. This is why a d20 system produces heroic upsets and improbable disasters, while a system rolling 3d6 produces competent characters who mostly perform as expected. Neither is better; they are different games, and the difference is entirely in the distribution.

Why physical dice are less fair than you think

Cheap plastic dice are meaningfully biased, and the reasons are mundane. The pips are drilled out and the resulting hollows are unevenly filled, so a six-pip face is lighter than a one-pip face and the die tends to land six-up. Injection moulding leaves a sprue mark and slight asymmetries. Dice that have been rolled thousands of times develop rounded edges unevenly. Casinos take this seriously: their dice are precision-machined to tight tolerances, have flush inlaid pips of the same density as the body, are transparent so tampering is visible, and are retired on a schedule. A virtual roll has none of these problems, which makes it — genuinely, if unromantically — fairer than the dice in most people's game boxes.